TY - BOOK ID - 14663217 TI - Symmetry in mechanics : a gentle, modern introduction PY - 2001 SN - 1461201896 0817641459 3764341459 9780817641450 PB - Boston (Mass.): Birkhäuser, DB - UniCat KW - Global differential geometry. KW - Mathematics. KW - Topological Groups. KW - Mechanics, Analytic KW - Geometry, Differential KW - Engineering & Applied Sciences KW - Applied Mathematics KW - 548.12 KW - Theory of symmetry. Theory of original forms in general KW - 548.12 Theory of symmetry. Theory of original forms in general KW - Differential geometry KW - Analytical mechanics KW - Kinetics KW - Classical mechanics. Field theory KW - Mechanics, Analytic. KW - Geometry, Differential. KW - Topological groups. KW - Lie groups. KW - Applied mathematics. KW - Engineering mathematics. KW - Differential geometry. KW - Mathematical physics. KW - Topological Groups, Lie Groups. KW - Applications of Mathematics. KW - Differential Geometry. KW - Theoretical, Mathematical and Computational Physics. KW - Physical mathematics KW - Physics KW - Engineering KW - Engineering analysis KW - Mathematical analysis KW - Groups, Lie KW - Lie algebras KW - Symmetric spaces KW - Topological groups KW - Groups, Topological KW - Continuous groups KW - Mathematics UR - https://www.unicat.be/uniCat?func=search&query=sysid:14663217 AB - "And what is the use," thought Alice, "of a book without pictures or conversations in it?" -Lewis Carroll This book is written for modem undergraduate students - not the ideal stu­ dents that mathematics professors wish for (and who occasionally grace our campuses), but the students like many the author has taught: talented but ap­ preciating review and reinforcement of past course work; willing to work hard, but demanding context and motivation for the mathematics they are learning. To suit this audience, the author eschews density of topics and efficiency of presentation in favor of a gentler tone, a coherent story, digressions on mathe­ maticians, physicists and their notations, simple examples worked out in detail, and reinforcement of the basics. Dense and efficient texts play a crucial role in the education of budding (and budded) mathematicians and physicists. This book does not presume to improve on the classics in that genre. Rather, it aims to provide those classics with a large new generation of appreciative readers. This text introduces some basic constructs of modern symplectic geometry in the context of an old celestial mechanics problem, the two-body problem. We present the derivation of Kepler's laws of planetary motion from Newton's laws of gravitation, first in the style of an undergraduate physics course, and x Preface then again in the language of symplectic geometry. No previous exposure to symplectic geometry is required: we introduce and illustrate all necessary con­ structs. ER -